The claim is trivially true, isn't it? I.e.: a) milk is nutritious, and nutrition is essential for growth; b) it's not necessary (some people grow tall without milk, from other sources of nutrition); c) it's not sufficient (you need other types/sources of nutrition as well).
– ChrisWFeb 15 '15 at 11:12

1 Answer
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There is association between cow's milk consumption and height gain in children per three studies listed below. "Height gain in children may depend not only on the calcium in cow milk but also on some of its bioactive components".

Per a 2004 study 'Effect of cow milk consumption on longitudinal height gain in children' by Tomoo Okada, researchers observed a height gain in the children who consumed a high amount of cow milk.

Per a 2009 study 'Dairy Consumption and Female Height Growth: Prospective Cohort Study' by Catherine S. Berkey et.al., researchers concluded that off the foods/nutrients studied, dairy protein had the strongest association with height growth. "These findings suggest that a factor in the nonlipid phase of milk, but not protein itself, has growth-promoting action in girls."

Per a 2015 study 'Milk intake, height and body mass index in preschool children' by Mark D DeBoer et.al., researchers concluded that "in a cohort of children at age 4 years, the volume of milk consumed was associated with higher weight status and taller stature, while at 5 years, higher milk consumption continued to be associated with taller stature." This study supported current American Academy of Pediatrics recommendations that pre-school children should consume two milk servings daily.

However caution should be exercised since some studies such as 'Childhood Growth and Breast Cancer' in 2003 and 'Growth Patterns and the Risk of Breast Cancer in Women' in 2004 suggest that more rapid childhood height growth may be a factor in the development of cancer, especially breast cancer in women since dietary factors may promote more rapid prepubertal height growth, which may be a critical period for the development of breast cancer or other adult diseases.

"dairy protein consumption" is not the same thing as "cow's milk". Your studies cite "milk consumption" and you've added your opinion that it must be the protein. More appropriately, you should say "cow's milk intake".
– fredsbendJul 13 '15 at 19:51

More likely the cause, if we were to study any causation, Vitamin D, which is added to most cow's milk in America, does encourage bone growth in children. The question would be, does the added Vit. D to cow's milk cause height growth in children?
– fredsbendJul 13 '15 at 19:53

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Per results of the 2009 study, "Baseline milk and dairy protein predicted taller adults. Dairy protein was more important than dairy fat, for all outcomes. Nondairy animal protein and vegetable protein were never significant, nor were nondairy animal fat and vegetable fat." Per discussion of the same study "These longitudinal analyses of three different height growth outcomes provided evidence that dairy milk and yogurt intakes and dairy protein consumption, but not protein from other sources (nondairy animal and vegetable) or dietary fat or cheese, promote height growth".
– pericles316Jul 14 '15 at 9:51

I guess I'll have to look more closely at their methodology.
– fredsbendJul 14 '15 at 15:05

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This is quite interesting, but I think your answer should note the size of the effects claimed by those studies. Wikipedia says human children grow at ~2.8 inches/year average as teens. The studies claim gains of about 0.1 inches per year for teens, and 1cm/year for 4 year olds. Also, on careful reading, the first source you cite is very confusing. The numbers they give show a significantly larger gain in hight for the group consuming LESS milk! The conclusions at the end suggest this is a typo, but it's very odd.
– John DoucetteJul 14 '15 at 22:35